Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - 2-convexity and 2-concavity in Schatten ideals.
AU - Jameson, Graham J. O.
N1 - http://journals.cambridge.org/action/displayJournal?jid=PSP The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 120 (4), pp 697-701 1996, © 1996 Cambridge University Press.
PY - 1996/11
Y1 - 1996/11
N2 - The properties p-convexity and q-concavity are fundamental in the study of Banach sequence spaces (see [L-TzII]), and in recent years have been shown to be of great significance in the theory of the corresponding Schatten ideals ([G-TJ], [LP-P] and many other papers). In particular, the notions 2-convex and 2-concave are meaningful in Schatten ideals. It seems to have been noted only recently [LP-P] that a Schatten ideal has either of these properties if the underlying sequence space has. One way of establishing this is to use the fact that if (E, E) is 2-convex, then there is another Banach sequence space (F, F) such that x; = x2F for all x ε E. The 2-concave case can then be deduced using duality, though this raises some difficulties, for example when E is inseparable.
AB - The properties p-convexity and q-concavity are fundamental in the study of Banach sequence spaces (see [L-TzII]), and in recent years have been shown to be of great significance in the theory of the corresponding Schatten ideals ([G-TJ], [LP-P] and many other papers). In particular, the notions 2-convex and 2-concave are meaningful in Schatten ideals. It seems to have been noted only recently [LP-P] that a Schatten ideal has either of these properties if the underlying sequence space has. One way of establishing this is to use the fact that if (E, E) is 2-convex, then there is another Banach sequence space (F, F) such that x; = x2F for all x ε E. The 2-concave case can then be deduced using duality, though this raises some difficulties, for example when E is inseparable.
U2 - 10.1017/S0305004100001651
DO - 10.1017/S0305004100001651
M3 - Journal article
VL - 120
SP - 697
EP - 701
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
SN - 0305-0041
IS - 4
ER -